# Equations & Simplification Problem Set

Math 209 College Mathematics II

Quiz

Instructions: Show work in order to receive partial credit. The number within parentheses represents the point value. There is a maximum of 60 points. The due date is Monday February 22, 2010

1. (4) Factor the following trinomial completely: 6x2 + 21x - 45.

2. (4) Evaluate the rational expression given the indicated value of the variable when x = -2.

3. (4) Simplify by removing a factor equal to one.

4. (4) Divide and, if possible, simplify.

5. Perform the indicated operations. Simplify when possible.

6. (4) Find the lowest common denominator, LCD.

7. (4) Find the domain of the rational expression.

8. A ball is dropped from a height of 64 feet. Its height above the earth in feet is given

by h(t) = -16t2 + 64, where t is the number of seconds after it is dropped.

a) (2) Find h(1)

b) (2) How long does it take the ball to fall to the earth?

9. (4) Simplify the complex fraction.

10. (4) Solve the equation.

11. (4) To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist's estimate of the size of the bear population?

12. (4) Solve the equation 3u2 = 8u - 5.

13. (4) Solve the formula for the indicated variable A = P + Prt for t.

14. (4) Solve the equation.

Please see the attachment.

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#### Solution Summary

The solution provides step by step method for the calculation of simplification of expressions and roots of equations. Formula for the calculation is also included. This solution is presented in an attached Word document.